Hello,

I am not a student of graph theory but I have a question regarding Kruskal's algorithm. I was wondering that with a simple weighted graph where there were multiple minimum weight spanning trees, depending on the choices that one makes with Kruskal's algorithm, would it be possible to find all possible minimum weight spanning trees or is there a case where one of the minimum weight spanning trees cannot be obtained?

I haven't come across a proof and I have been attempting various graphs with many cycles in an attempt to limit how kruskal would operate but always Kruskal's algorithm will produce all possible minimum weight spanning trees depending on the choices made. Is there an example I am missing?

Thanks for your help!